Enumerability - Decidability Computability: An Introduction to the Theory of Recursive Functions
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1969
|
| Ausgabe: | Second revised Edition |
| Schriftenreihe: | Die Grundlehren der mathematischen Wissenschaften, In Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete
127 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Once we have accepted a precise replacement of the concept of algorithm, it becomes possible to attempt the problem whether there exist well-defined collections of problems which cannot be handled by algorithms, and if that is the case, to give concrete cases of this kind. Many such investigations were carried out during the last few decades. The undecidability of arithmetic and other mathematical theories was shown, further the unsolvability of the word problem of group theory. Many mathematicians consider these results and the theory on which they are based to be the most characteristic achievements of mathematics in the first half of the twentieth century. If we grant the legitimacy of the suggested precise replacements of the concept of algorithm and related concepts, then we can say that the mathematicians have shown by strictly mathematical methods that there exist mathematical problems which cannot be dealt with by the methods of calculating mathematics. In view of the important role which mathematics plays today in our conception of the world this fact is of great philosophical interest. Post speaks of a natural law about the "limitations of the mathematicizing power of Homo Sapiens". Here we also find a starting point for the discussion of the question, what the actual creative activity of the mathematician consists in. In this book we shall give an introduction to the theory of algorithms |
| Beschreibung: | 1 Online-Ressource (XII, 250 p) |
| ISBN: | 9783642461781 9783642461804 |
| DOI: | 10.1007/978-3-642-46178-1 |
Internformat
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-46178-1 |
| edition | Second revised Edition |
| format | Electronic eBook |
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| isbn | 9783642461781 9783642461804 |
| language | English |
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| series | Die Grundlehren der mathematischen Wissenschaften, In Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| series2 | Die Grundlehren der mathematischen Wissenschaften, In Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| spelling | Hermes, Hans 1912-2003 Verfasser (DE-588)117712302 aut Enumerability - Decidability Computability An Introduction to the Theory of Recursive Functions by Hans Hermes Second revised Edition Berlin, Heidelberg Springer Berlin Heidelberg 1969 1 Online-Ressource (XII, 250 p) txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der mathematischen Wissenschaften, In Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 127 Once we have accepted a precise replacement of the concept of algorithm, it becomes possible to attempt the problem whether there exist well-defined collections of problems which cannot be handled by algorithms, and if that is the case, to give concrete cases of this kind. Many such investigations were carried out during the last few decades. The undecidability of arithmetic and other mathematical theories was shown, further the unsolvability of the word problem of group theory. Many mathematicians consider these results and the theory on which they are based to be the most characteristic achievements of mathematics in the first half of the twentieth century. If we grant the legitimacy of the suggested precise replacements of the concept of algorithm and related concepts, then we can say that the mathematicians have shown by strictly mathematical methods that there exist mathematical problems which cannot be dealt with by the methods of calculating mathematics. In view of the important role which mathematics plays today in our conception of the world this fact is of great philosophical interest. Post speaks of a natural law about the "limitations of the mathematicizing power of Homo Sapiens". Here we also find a starting point for the discussion of the question, what the actual creative activity of the mathematician consists in. In this book we shall give an introduction to the theory of algorithms Mathematics Mathematics, general Mathematik Rekursive Funktion (DE-588)4138367-9 gnd rswk-swf Berechenbarkeit (DE-588)4138368-0 gnd rswk-swf Aufzählbarkeit (DE-588)4800450-9 gnd rswk-swf Entscheidbarkeit (DE-588)4152398-2 gnd rswk-swf Algorithmentheorie (DE-588)4200409-3 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Rekursive Funktion (DE-588)4138367-9 s 2\p DE-604 Algorithmentheorie (DE-588)4200409-3 s 3\p DE-604 Algorithmus (DE-588)4001183-5 s 4\p DE-604 Berechenbarkeit (DE-588)4138368-0 s 5\p DE-604 Entscheidbarkeit (DE-588)4152398-2 s 6\p DE-604 Aufzählbarkeit (DE-588)4800450-9 s 7\p DE-604 Die Grundlehren der mathematischen Wissenschaften, In Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 127 (DE-604)BV049758308 127 https://doi.org/10.1007/978-3-642-46178-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hermes, Hans 1912-2003 Enumerability - Decidability Computability An Introduction to the Theory of Recursive Functions Die Grundlehren der mathematischen Wissenschaften, In Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete Mathematics Mathematics, general Mathematik Rekursive Funktion (DE-588)4138367-9 gnd Berechenbarkeit (DE-588)4138368-0 gnd Aufzählbarkeit (DE-588)4800450-9 gnd Entscheidbarkeit (DE-588)4152398-2 gnd Algorithmentheorie (DE-588)4200409-3 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4138367-9 (DE-588)4138368-0 (DE-588)4800450-9 (DE-588)4152398-2 (DE-588)4200409-3 (DE-588)4001183-5 (DE-588)4151278-9 |
| title | Enumerability - Decidability Computability An Introduction to the Theory of Recursive Functions |
| title_auth | Enumerability - Decidability Computability An Introduction to the Theory of Recursive Functions |
| title_exact_search | Enumerability - Decidability Computability An Introduction to the Theory of Recursive Functions |
| title_full | Enumerability - Decidability Computability An Introduction to the Theory of Recursive Functions by Hans Hermes |
| title_fullStr | Enumerability - Decidability Computability An Introduction to the Theory of Recursive Functions by Hans Hermes |
| title_full_unstemmed | Enumerability - Decidability Computability An Introduction to the Theory of Recursive Functions by Hans Hermes |
| title_short | Enumerability - Decidability Computability |
| title_sort | enumerability decidability computability an introduction to the theory of recursive functions |
| title_sub | An Introduction to the Theory of Recursive Functions |
| topic | Mathematics Mathematics, general Mathematik Rekursive Funktion (DE-588)4138367-9 gnd Berechenbarkeit (DE-588)4138368-0 gnd Aufzählbarkeit (DE-588)4800450-9 gnd Entscheidbarkeit (DE-588)4152398-2 gnd Algorithmentheorie (DE-588)4200409-3 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Rekursive Funktion Berechenbarkeit Aufzählbarkeit Entscheidbarkeit Algorithmentheorie Algorithmus Einführung |
| url | https://doi.org/10.1007/978-3-642-46178-1 |
| volume_link | (DE-604)BV049758308 |
| work_keys_str_mv | AT hermeshans enumerabilitydecidabilitycomputabilityanintroductiontothetheoryofrecursivefunctions |